\[ \int (f x)^{-1+m} \left (d+e x^m\right ) \left (a+b \log \left (c x^n\right )\right )^2 \, dx \]
Optimal antiderivative \[ \frac {2 b^{2} d \,n^{2} x \left (f x \right )^{-1+m}}{m^{3}}+\frac {b^{2} e \,n^{2} x^{1+m} \left (f x \right )^{-1+m}}{4 m^{3}}+\frac {b^{2} d^{2} n^{2} x^{1-m} \left (f x \right )^{-1+m} \ln \left (x \right )^{2}}{2 e m}-\frac {2 b d n x \left (f x \right )^{-1+m} \left (a +b \ln \left (c \,x^{n}\right )\right )}{m^{2}}-\frac {b e n \,x^{1+m} \left (f x \right )^{-1+m} \left (a +b \ln \left (c \,x^{n}\right )\right )}{2 m^{2}}-\frac {b \,d^{2} n \,x^{1-m} \left (f x \right )^{-1+m} \ln \left (x \right ) \left (a +b \ln \left (c \,x^{n}\right )\right )}{e m}+\frac {x^{1-m} \left (f x \right )^{-1+m} \left (d +e \,x^{m}\right )^{2} \left (a +b \ln \left (c \,x^{n}\right )\right )^{2}}{2 e m} \]
command
integrate((f*x)**(-1+m)*(d+e*x**m)*(a+b*ln(c*x**n))**2,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {output too large to display} \]
Sympy 1.8 under Python 3.8.8 output \[ \text {Timed out} \]_____________________________________________________